Problems that require solving the three-dimensional schrödinger equation can often be reduced to related one-dimensional problems. an example of this would be the particle in a cubical box. consider a cubical box with rigid walls (i. e., u (x, y, z) = ∞ outside of the cube) and edges of length l. the general solution for this problem is

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Avery Garrett

Mathematics

8 August, 15:44

Problems that require solving the three-dimensional schrödinger equation can often be reduced to related one-dimensional problems. an example of this would be the particle in a cubical box. consider a cubical box with rigid walls (i. e., u (x, y, z) = ∞ outside of the cube) and edges of length l. the general solution for this problem is

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Sneakers · Answer 1

The wavefunction for a particle in a one-dimension box is a well-known problem, which has as a solution:

Ψ (x) = √ (2/l) sin (nπx/l)

When the box has three dimensions, the general solution is simply the multiplication of the solutions for each dimension, therefore:

Ψ (x) = K · sin (n_x·π·x / l) · sin (n_y·π·y / l) · sin (n_z·π·z / l)